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Semidefinite Implementations of the Proximal Point Algorithm and Consequences for Progressive Decoupling in Optimization
Xudong Li, R. Tyrrell Rockafellar, Defeng Sun
The proximal point algorithm for finding a zero of a maximal monotone mapping is the engine that drives augmented Lagrangian methods and various splitting schemes in convex optimiz…
Maximal monotonicity of piecewise polyhedral mappings
Xudong Li, R. Tyrrell Rockafellar, Defeng Sun
Maximal monotone mappings that are piecewise polyhedral arise from subdifferentials of convex functions and saddle functions that are piecewise linear-quadratic and enter into algo…
Reaching an equilibrium of prices and holdings of goods through direct buying and selling
J. Deride, A. Jofré, R. T. Rockafellar
The Walras approach to equilibrium focuses on the existence of market prices at which the total demands for goods are matched by the total supplies. Trading activities that might i…
Second-order subdifferential calculus with applications to tilt stability in optimization
B. S. Mordukhovich, R. T. Rockafellar
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in f…